Counting statistics: A Feynman-Kac perspective

Counting statistics: a Feynman-Kac perspective.

By building upon a Feynman-Kac formalism, we assess the distribution of the number of collisions in a given region for a broad class of discrete-time random walks in absorbing and nonabsorbing media. We derive the evolution equation for the generating function of the number of collisions, and we complete our analysis by examining the moments of the distribution and their relation to the walker ...

Quantum Feynman-Kac perturbations

The Feynman-Kac formula

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...

First Order Feynman-Kac Formula

We study the parabolic integral kernel associated with the weighted Laplacian with a potential. For manifold with a pole we deduce formulas and estimates for the derivatives of the Feynman-Kac kernels and their logarithms, these are in terms of a ‘Gaussian’ term and the semi-classical bridge. Assumptions are on the Riemannian data. AMS Mathematics Subject Classification : 60Gxx, 60Hxx, 58J65, 5...

A Feynman-Kac Formula for Unbounded Semigroups

We prove a Feynman-Kac formula for Schrödinger operators with potentials V (x) that obey (for all ε > 0) V (x) ≥ −ε|x| − Cε. Even though e is an unbounded operator, any φ, ψ ∈ L with compact support lie in D(e) and 〈φ, eψ〉 is given by a Feynman-Kac formula.